Solve.
-The volume of wood in a tree varies jointly as the height of the tree and the square of the distance around the tree trunk. If the volume of wood is 15.84 cubic feet when the height is 22 feet and the distance around the trunk Is 3 feet, what is the volume of wood obtained from a tree that is 33 feet tall having a measurement of 5 feet Around the trunk?
A) 75 cubic feet
B) 70 cubic feet
C) 58 cubic feet
D) 66 cubic feet

Question

Quizplus · Accepted Answer

The volume of wood in a tree $V$ varies jointly as the height $h$ of the tree and the square of the distance $d$ around the tree trunk, which can be represented by the equation $V = k \cdot h \cdot d^2$, where $k$ is the constant of variation. Given $V = 15.84$ cubic feet when $h = 22$ feet and $d = 3$ feet, we can find $k$ by substituting these values into the equation: $15.84 = k \cdot 22 \cdot 3^2$. Solving for $k$ gives $k = 0.08$. To find the volume of wood from a tree that is 33 feet tall with a 5 feet circumference, substitute $h = 33$, $d = 5$, and $k = 0.08$ into the equation: $V = 0.08 \cdot 33 \cdot 5^2 = 66$ cubic feet.

Solve. -The Volume of Wood in a Tree Varies Jointly as as the Height